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could be! but if I see x^k / k! , I cant resist the temptation.. especially when there's a π !
The sum is a nice corollary, but not what I'd seek to explain. First, it's rare that one should add a length, an area, a volume... it goes against dimensional analysis. Second, e^pi is not a number I know anything about.
I agree, but I was just thinking we could attach a dimensional factor (1/L)^n if we wanted too which would leave the exponential in tact
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If you sum over the volumes of all 2k-dimensional unit spheres, that sum converges to e^π.
I have no idea why this should be true..
